The structure of one-relator relative presentations and their centres

DOI10.1515/JGT.2009.024zbMath1203.20030arXivmath/0701308OpenAlexW3104801526MaRDI QIDQ3401166

Anton A. Klyachko

Publication date: 29 January 2010

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701308

zbMATH Keywords

asphericityone-relator groupsamalgamated productsrelative presentationscentre

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Topological methods in group theory (57M07) Extensions, wreath products, and other compositions of groups (20E22) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Cancellation theory of groups; application of van Kampen diagrams (20F06) Algebraic geometry over groups; equations over groups (20F70)

Related Items (4)

Commutator length of powers in free products of groups ⋮ A class of Artin groups in which the \(K( \pi ,1)\) conjecture holds ⋮ Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator. ⋮ On a conjecture in Artin groups

Cites Work

• How to generalize known results on equations over groups.
• Equations over groups, and groups with one defining relation
• Torsion-free group without unique product property
• The surjectivity problem for one-generator, one-relator extensions of torsion-free groups
• The centre of groups with one defining relator
• The isomorphism problem for one-relator groups with non-trivial centre
• The center of a group with a single defining relation
• The Quotient of a Free Product of Groups by a Single High-Powered Relator. III. The Word Problem
• The Kervaire-Laudenbach Conjecture and Presentations of Simple Groups
• Free subgroups of one-relator relative presentations
• A Simple Example of a Torsion-Free, Non Unique Product Group
• The solution of length three equations over groups
• Aspherical relative presentations
• A funny property of sphere and equations over groups
• Free Bases for Normal Subgroups of Free Groups
• On the structure of one-relator products of locally indicable groups with centre

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